Finite Group Databasebeta

← #14302967

Subgroups — #14302967

Order 1920.

628 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756285C211yesmaximal, characteristic
2#11754213C211yesmaximal, characteristic, complemented
3#11748429C211yesmaximal, characteristic
4#11748428C211yesmaximal, characteristic
5C2×#90963C211yesmaximal, characteristic, complemented
6C5×#4531C211yesmaximal, characteristic, complemented
7C3×#64751C211yesmaximal, characteristic, complemented
8#10599501—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91786—22no—
13#91775—22no—
14#91764C412yescomplemented
15#91758C412yescomplemented
16C5×#926C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91532—22no—
21#91340—22no—
22#91333—22no—
23#90981—22no—
24#90980—22no—
25#90963—22no—
26#68708—51nomaximal, Hall
27#65860—31no—
28#65850—31no—
29#65428—31no—
30C2×#3956—31no—
31#65294—31no—
32C5×H(3,ℤ/4)—31no—
33#64751D311yescharacteristic, complemented
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220—21no—
36C22×Dic15D412yes—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41C2×D60C2×C411yescharacteristic
42C2×C4×D15—21no—
43C2×Dic30—21no—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C2×Dic30—21no—
47C2×Dic30C2×C411yescharacteristic
48C2×Dic30C2×C412yes—
49C2×Dic30D412yes—
50C3×C5×C4⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2×C412yes—
53#6714—24no—
54C4⋊Dic15—24no—
55C5×#217—21no—
56C5×C4⋊Dic3—21no—
57C4×C5×Dic3D412yes—
58C5×#208—21no—
59C5×#208—21no—
60C2×C5×C3⋊C8—21no—
61C3×C22⋊Dic5—21no—
62C3×C4⋊Dic5—21no—
63C3×C4×Dic5D412yes—
64C3×#681—21no—
65C3×#681—21no—
66C2×C3×#168—21no—
67#6669—24no—
68Dic3×Dic5—24no—
69#5526—51no—
70#5516—51no—
71#5139—51no—
72C2×#824—51no—
73#5005—51no—
74C3×H(3,ℤ/4)—51no—
75#4531D511yescharacteristic, complemented
76C2×#709—31no—
77C22×Dic10—31no—
78C2×C5×M16—31no—
79C5×#117—31no—
80C5×#117C2×D311yescharacteristic
81#4072C2×D311yescharacteristic
82C2×#681C2×D311yescharacteristic
83#4043—62no—
84#4033—62no—
85#4032—62no—
86#4023—62no—
87#4021—32no—
88#4015—32no—
89C4×Dic10—62no—
90#3957—62no—
91#3956—62no—
92#3937—62no—
93#1912—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103#1220—41no—
104#1220—41no—
105C2×Dic15—22no—
106C2×Dic15—22no—
107C2×Dic15—21no—
108C2×Dic15C22⋊C414yes—
109D60—21no—
110D60—21no—
111C4×D15—41no—
112C4×D15—41no—
113Dic30—22no—
114Dic30—22no—
115Dic30—22no—
116Dic30—22no—
117Dic30—21no—
118Dic30—21no—
119C2×C5×Dic3—22no—
120C2×C3×Dic5—22no—
121C3×#168—41no—
122C5×C3⋊C8—41no—
123C2×#235—51no—
124C22×Dic6—51no—
125C2×C3×M16—51no—
126C3×#117—51no—
127C3×#117C2×D511yescharacteristic
128#926C2×D511yescharacteristic
129C2×#208C2×D511yescharacteristic
130#897—102no—
131#887—102no—
132#886—102no—
133#877—102no—
134#875—52no—
135#869—52no—
136C4×Dic6—102no—
137#825—102no—
138#824—102no—
139#805—102no—
140C22×C4×C5C22×D311yescharacteristic
141C2×C22⋊D5—61no—
142C22×Dic5—32no—
143#709—61no—
144#709—61no—
145#709—61no—
146#709—61no—
147C2×D20—31no—
148C2×C4×D5—61no—
149C2×Dic10—32no—
150C2×Dic10—32no—
151C2×Dic10—31no—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C2×Dic10—61no—
156C5×M16—61no—
157C5×M16—61no—
158C2×C5×C8—61no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—21no—
162C5×C22⋊C4—61no—
163C42×C5—32no—
164C42×C5C4×D312yes—
165C22⋊Dic5—21no—
166#685—64no—
167C4⋊Dic5—21no—
168C4⋊Dic5—64no—
169#683—64no—
170C4×Dic5—64no—
171C4×Dic5D1212yes—
172#681—21no—
173#681—21no—
174C2×#168—21no—
175#536—151no—
176#519—151no—
177#421—151no—
178#421—151no—
179C2×#101—151no—
180H(3,ℤ/4)—31no—
181H(3,ℤ/4)—51no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×D15—42no—
187C2×D15—41no—
188C3×C4×C5—42no—
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12111yescharacteristic
192C3×C4×C5#12111yescharacteristic
193Dic15—24no—
194Dic15—41no—
195C3×Dic5—42no—
196C5×Dic3—42no—
197C22×C3×C4C22×D511yescharacteristic
198C2×#67—101no—
199C22×Dic3—52no—
200#235—101no—
201#235—101no—
202#235—101no—
203#235—101no—
204C2×D12—51no—
205C2×C4×D3—101no—
206C2×Dic6—52no—
207C2×Dic6—52no—
208C2×Dic6—51no—
209C2×Dic6—101no—
210C2×Dic6—101no—
211C2×Dic6—101no—
212C2×Dic6—101no—
213C3×M16—101no—
214C3×M16—101no—
215C2×C3×C8—101no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—101no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—101no—
220C3×C42—52no—
221C3×C42C4×D512yes—
222#217—21no—
223(C2×D3)⋊C4—104no—
224C4⋊Dic3—21no—
225C4⋊Dic3—104no—
226Dic3⋊C4—104no—
227C4×Dic3—104no—
228C4×Dic3D2012yes—
229#208—21no—
230#208—21no—
231C2×C3⋊C8—21no—
232C23×C5D3×D411yescharacteristic
233C22×D5—61no—
234C2×C4×C5—22no—
235C2×C4×C5—62no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C2×C4×C5C2×D1211yescharacteristic
238C2×C4×C5#23511yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5D3×D411yescharacteristic
241C2×C4×C5#23911yescharacteristic
242C22⋊D5—121no—
243C22⋊D5—121no—
244C2×Dic5—22no—
245C2×Dic5—34no—
246C2×Dic5—62no—
247C2×Dic5—62no—
248C2×Dic5—61no—
249D20—61no—
250D20—61no—
251C4×D5—121no—
252C4×D5—121no—
253Dic10—62no—
254Dic10—62no—
255Dic10—62no—
256Dic10—62no—
257Dic10—61no—
258Dic10—61no—
259C5×C8—121no—
260#168—41no—
261C2×#41—151no—
262C22×Q8—151no—
263C2×M16—31no—
264C2×M16—51no—
265C4⋊Q8—152no—
266#124—152no—
267#123—302no—
268C22⋊Q8—302no—
269C4×Q8—302no—
270C4×Q8—302no—
271#117—31no—
272#117—51no—
273#117—302no—
274#117D3×D511yescharacteristic
275#104—302no—
276#104—302no—
277#101—302no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38611yescharacteristic
282D15—81no—
283C23×C3D4×D511yescharacteristic
284C22×D3—101no—
285C2×C3×C4—22no—
286C2×C3×C4—102no—
287C2×C3×C4C2×C4×D511yescharacteristic
288C2×C3×C4C2×D2011yescharacteristic
289C2×C3×C4#70911yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4D4×D511yescharacteristic
292C2×C3×C4#71311yescharacteristic
293#67—201no—
294#67—201no—
295C2×Dic3—22no—
296C2×Dic3—54no—
297C2×Dic3—102no—
298C2×Dic3—102no—
299C2×Dic3—101no—
300D12—101no—
301D12—101no—
302C4×D3—201no—
303C4×D3—201no—
304Dic6—102no—
305Dic6—102no—
306Dic6—102no—
307Dic6—102no—
308Dic6—101no—
309Dic6—101no—
310C3×C8—201no—
311C3⋊C8—41no—
312C22×C5—41no—
313C22×C5D3×C22⋊C411yescharacteristic
314C22×C5#88211yescharacteristic
315C22×C5#89411yescharacteristic
316C2×D5—122no—
317C2×D5—121no—
318C4×C5—42no—
319C4×C5—122no—
320C4×C5C4×D1211yescharacteristic
321C4×C5#88411yescharacteristic
322C4×C5#89311yescharacteristic
323C4×C5#89511yescharacteristic
324Dic5—42no—
325Dic5—64no—
326Dic5—121no—
327#41—301no—
328#41—301no—
329#41—301no—
330#41—301no—
331C2×Q8—152no—
332C2×Q8—152no—
333C2×Q8—151no—
334C2×Q8—301no—
335C2×Q8—301no—
336C2×Q8—301no—
337C2×Q8—301no—
338C2×D4—151no—
339C2×D4—301no—
340C22×C4—152no—
341C22×C4—301no—
342C22×C4C2×D3×D511yescharacteristic
343M16—61no—
344M16—61no—
345M16—101no—
346M16—101no—
347C2×C8—61no—
348C2×C8—101no—
349C4⋊C4—21no—
350C4⋊C4—61no—
351C4⋊C4—101no—
352C4⋊C4—304no—
353C4⋊C4—304no—
354C22⋊C4—21no—
355C22⋊C4—61no—
356C22⋊C4—101no—
357C22⋊C4—304no—
358C42—32no—
359C42—52no—
360C42—304no—
361C42#120012yes—
362C3×C5#191211yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3D5×C22⋊C411yescharacteristic
365C22×C3#402811yescharacteristic
366C22×C3#404011yescharacteristic
367C2×D3—202no—
368C2×D3—201no—
369C3×C4—42no—
370C3×C4—202no—
371C3×C4C4×D2011yescharacteristic
372C3×C4#403011yescharacteristic
373C3×C4#403911yescharacteristic
374C3×C4#404111yescharacteristic
375Dic3—42no—
376Dic3—104no—
377Dic3—201no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5#466511yescharacteristic
382D5—241no—
383C23—301no—
384C23#679011yescharacteristic
385Q8—302no—
386Q8—302no—
387Q8—302no—
388Q8—302no—
389Q8—301no—
390Q8—301no—
391D4—301no—
392D4—301no—
393D4—601no—
394D4—601no—
395C2×C4—22no—
396C2×C4—62no—
397C2×C4—102no—
398C2×C4—154no—
399C2×C4—302no—
400C2×C4—302no—
401C2×C4—301no—
402C2×C4—601no—
403C2×C4—601no—
404C2×C4#676911yescharacteristic
405C2×C4#677311yescharacteristic
406C2×C4D5×D1211yescharacteristic
407C2×C4D3×D2011yescharacteristic
408C2×C4C2×#120011yescharacteristic
409C2×C4#679011yescharacteristic
410C8—121no—
411C8—201no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3#6495411yescharacteristic
416D3—401no—
417C5#6870811yescharacteristic, complemented, Sylow
418C22—41no—
419C22—602no—
420C22—601no—
421C22#9143311yescharacteristic
422C22#9147611yescharacteristic
423C22#9156111yescharacteristic
424C4—42no—
425C4—122no—
426C4—202no—
427C4—304no—
428C4—601no—
429C4#9141811yescharacteristic
430C4#9142011yescharacteristic
431C4#9142811yescharacteristic
432C4#9145911yescharacteristic
433C3#1059950111yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—1201no—
438C2#1174890411yescharacteristic
subgroupG/H
centerC2#11748904
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1912
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11754213C2semidirect
5. C2×#90963C2semidirect
6. C5×#4531C2semidirect
7. C3×#64751C2semidirect
14. #91764C4semidirect
15. #91758C4semidirect
33. #64751D3semidirect
75. #4531D5semidirect
362. C3×C5#1912semidirect
417. C5#68708semidirect
433. C3#10599501semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117562852
#117542132
#117484292
#117484282
C2×#909632
C5×#45312
C3×#647512
#105995013
#687085